(a) There are initially 500 rabbits (x) and 200 faxes (y) on Farmer Oat's property. Us...

(a) There are initially 500 rabbits (x) and 200 faxes (y) on Farmer Oat's property. Use Polymath or MATLAB to plot the oncentration of faxes and rabbits as a function of time for a period of up to 500 days. The predator–prey relationships are given by he following set of coupled ordinary differential equations:

Constant for growth of rabbits k1 = 0.02 day−1

Constant for death of rabbits k2 = 0.00004/(day × no. of faxes)

Constant for growth of faxes after eating rabbits k3 = 0.0004/(day × no. of rabbits)

Constant for death of faxes k4 = 0.04 day−1

What do your results look like for the case of k3 = 0.00004/(day × no. of rabbits) and tfinal = 800 days? Also plot the number of faxes versus the number of rabbits. Explain why the curves look the way they do.

Vary the parameters k1, k2 , k3 , and k4 . Discuss which parameters can or cannot be larger than others. Write a paragraph describing what you find.

(b) Use Polymath or MATLAB to solve the following set of nonlinear algebraic equations:

with initial guesses of x = 2, y = 2. Try to become familiar with the edit keys in Polymath and MATLAB. See the CD-ROM for instructions.

Screen shots on how to run Polymath are shown at the end of Summary Notes for Chapter 1 on the CD-ROM and on the web.